In this paper we consider the class of convex optimization problems with affine inequality constraints and focus hereby on the class of quadratic programs. We propose a smooth vector field that is constructed such that its trajectories converge to the saddle point of the Lagrangian function associated to the convex optimization problem. We establish global asymptotic stability as well as exponential stability under mild assumptions for different variants of the vector field and propose a continuous-time Nesterov method.